Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in PYTHON3):

Solution:
# n = int(input())
# count = 0


# def increase(A):
#     for i in range(len(A) - 1):
#         if A[i] < A[i+1]:
#             print(A[i])
#             print(A[i+1])
#             return False
#         return True


# def main(h, p):
#     maximum = max(h)
#     indexMax = h.index(maximum)
#     h[indexMax] = p[0]
#     p.pop(0)
#     p.insert(maximum)
#     return h, p


# for i in range(1):
#     h = [int(i)for i in input().split(" ")]
#     p = [int(i)for i in input().split(" ")]

# print(p)
# print(h)
# print(increase(p))
# if increase(p) == True:
#     print(0)

# # while increase(p) == False:
# #     count += 1
# #     newh, newp = main(h, p)
# #     p = newp
# #     h = newh
# # print(count)
n = int(input())
print(n//2 + 1)
for i in range(1, n+1):
    if i % 2 == 0:
        m = int(i//2)
        print(f'{m} {m+1}')
    else:
        m = int(i//2)
        print(f'{m+1} {m+1}')